Soil Physics 2010

Stress

• Stress is a force per unit area: N m-2

• This is also a pressure. The SI unit of pressure is the Pascal: 1 Pa = 1 N m-2

• 1 N is the force required to accelerate 1 kg by 1 m s-2, so in earth’s gravity (g = 9.81 m s-2), 1/9.81 kg would exert a pressure of 1 Pa if applied over 1 m2.

0.1 kg

1 m

1 g

Soil Physics 2010

Pressure

• 1 Pa = 1 N m-2 = 1 (kg m)/(s2 m2) = 1 kg m-1 s-2

• What is atmospheric pressure?

• g * (Mass of atmosphere above 1 m2) = 101,325 Pa ≈ 101.3 kPa ≈ 0.1 MPa

• Same force as a column of water 10.1 m high

• ≈ 14.7 psi (pounds / inch2)

0.1 kg

1 m1 g

Soil Physics 2010

Stresses

• 4 Stresses commonly encountered:

•Compressive s

• Tensile s

• Shear t

• Torsion (not typical in soil)

Soil Physics 2010

Kinds of behavior under stress

• Elastic materials regain their pre-stress formExample: rubber

• Plastic materials remain in stressed formExample: modeling clay

• Viscous materials deform slowlyExample: tar

• Brittle materials fracture under stressExample: brick

• Soils have aspects of all of these

Soil Physics 2010

Strain (elastic & plastic)

• Strain is deformation (e.g. in response to stress)

• Often given as e ≡ DL / L0 : a relative change in length (dimensionless)

• Young’s modulus is the ratio: E ≡ s / = e s L0 / DL

L0

DL

Original height

L0 – DL:

Height after compression

Soil Physics 2010

Stress – strain curves I

Hooke’s Law:

e sFor elastic materials:

L0

DL

F

Strain e, DL/L0

Str

ess s,

F/A

Slope is E: Young’s modulus

E ≡ s / e, so

e = s / E

L0

DL

F

Strain e, DL/L0

Str

ess s,

F/A

Soil Physics 2010

Stress – strain curves IIFor many materials

(including soil, sometimes):Ela

stic

FailurePlastic Material has

sheared or fractured

Soil strength

1.2

1.6

2.0

2.4

5 10 15 20w

rb

saturation, mass basis

w

r b 100%

75%

90%

Soil Physics 2010

Proctor Compaction

Test

Water gets in the way

No lubrication

Optimal

• Soil strength is resistance to shear stress

• Strength depends mainly on:

1. Bulk density

Soil strength

1.2

1.6

2.0

2.4

5 10 15 20w

rb

w

r b 100%

75%

90%

Soil Physics 2010

More force needed

Less force needed

Harder to compact when dry

• Soil strength is resistance to shear stress

• Strength depends mainly on:

1. Bulk density

2. Wetness

Soil strength

• Soil strength is resistance to shear stress

• Strength depends mainly on:

1. Bulk density

2. Wetness

Soil Physics 2010

When the soil is saturated, some stress is borne by the water:

se = st – p se: effective stress (Terzaghi’s

st: total stress equation)

p: water pressure

st

Soil Physics 2010

Soil strength

• Soil strength is resistance to shear stress

• Strength depends mainly on:

1. Bulk density

2. Wetness

3. Particle size distribution

10110010-110-210-310-4

GradualAbruptPoorly GradedGradual distributions

tend to be stronger: tighter grain packing

Soil Physics 2010

Basic laws of friction:

Pull

1. friction normal force

Normal force

Support

Friction

2. friction is not affected by contact area (ideal case)

3. friction is not affected by velocity (for small velocities)

Soil Physics 2010

Shear test How strong is this soil?How hard is it to break this soil?

Measure force needed to breakRepeat for different normal forces

Apply normal

force

Soil Physics 2010

Direct shear(unconfined shear)

Soil Physics 2010

Direct shear(unconfined shear)